Strong-Base-Assisted Synthesis of a Crystalline Covalent Triazine Framework with High Hydrophilicity via Benzylamine Monomer for Photocatalytic Water Splitting

Methods to synthesize crystalline covalent triazine frameworks (CTFs) are limited and little attention has been paid to development of hydrophilic CTFs and photocatalytic overall water splitting. A route to synthesize crystalline and hydrophilic CTF-HUST-A1 with a benzylamine-functionalized monomer is presented. The base reagent used plays an important role in the enhancement of crystallinity and hydrophilicity. CTF-HUST-A1 exhibits good crystallinity, excellent hydrophilicity, and excellent photocatalytic activity in sacrificial photocatalytic hydrogen evolution (hydrogen evolution rate up to 9200 μmol g⁻¹ h⁻¹). Photocatalytic overall water splitting is achieved by depositing dual co-catalysts in CTF-HUST-A1, with H₂ evolution and O₂ evolution rates of 25.4 μmol g⁻¹ h⁻¹ and 12.9 μmol g⁻¹ h⁻¹ in pure water without using sacrificial agent.     

Existence of Global Weak Solutions for Coupled Thermoelasticity under Non-Linear Boundary Conditions

The existence of global weak solutions for coupled thermoelasticity with non-linear contact boundary conditions corresponding to the friction problem is considered. The time-continuous Galerkin method and a priori estimates obtained with Gronwall's inequality in connection with embedding theorems are applied to accomplish a straightforward generalization of one of the results proved by Martins and Oden 9.     

A Porous Tricyclooxacalixarene Cage Based on Tetraphenylethylene

A quadrangular prismatic tricyclooxacalixarene cage 1 based on tetraphenylethylene (TPE) was efficiently synthesized by a one‐pot S_NAr condensation reaction. As a result of the porous internal structure in the solid state, cage 1 exhibited a good CO₂ uptake capacity of 12.5 wt % and a high selectivity for CO₂ over N₂ adsorption of 80 (273 K, 1 bar) with a BET surface area of 432 m² g^?1. Formation of cage 1 led to the fluorescence of TPE being switched on in solution. The system was employed as a single‐molecule platform to study the mechanism of aggregation‐induced emission (AIE) by examining the restriction of intramolecular rotation (RIR).     

On division subrings normalized by almost subnormal subgroups in division rings

Periodica Mathematica Hungarica - Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ of D. The...     

Non-Convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a nonconvex optimization problem. This article shows a remarkable result: despite the nonconvexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of nonconvex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for nonconvex optimization and a novel way of exploiting nonconvexity for statistical inference.     

Division Algebras with Left Algebraic Commutators

Let D be a division algebra with center F and K a (not necessarily central) subfield of D. An element a ∈ D is called left algebraic (resp. right algebraic) over K, if there exists a non-zero left polynomial a ₀ + a ₁ x + ? + a _n x ⁿ (resp. right polynomial a ₀ + x a ₁ + ? + x ⁿ a _n ) over K such that a ₀ + a ₁ a + ? + a _n a ⁿ = 0 (resp. a ₀ + a a ₁ + ? + a ⁿ a _n ). Bell et al. proved that every division algebra whose elements are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. In this paper we generalize this result and prove that every division algebra whose all multiplicative commutators are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite provided that the center of division algebra is infinite. Also, we show that every division algebra whose multiplicative group of commutators is left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. Among other results we present similar result regarding additive commutators under certain conditions.     

Recent Development of Hypercrosslinked Microporous Organic Polymers

Hypercrosslinked polymers (HCPs) are currently receiving great interest due to their easy preparation, high chemical and thermal stability, and low cost. Combined with the lightweight properties and high surface areas HCPs can be considered as promising materials for gas storage and separation, catalysis, and heavy metal ions removal in wastewater treatment. This Feature Article summarizes strategies for the preparation of HCPs, comprising the post‐crosslinking of “Davankov‐type” resins, direct polycondensation of aromatic chloromethyl (or hydroxymethyl) monomers, and knitting aromatic compound polymers (KAPs). The HCPs applications, such as H₂ storage, CO₂ capture, and heterogeneous catalysis, are also discussed throughout in the article. Finally, the outlook of this research area is given.